In this study, a novel and integrated strategy is proposed to investigate the problem of low production rate of gas well in a supergiant gas condensate reservoir. In this strategy, the nodal analysis approach is applied for production optimization and performance assessment of a real inclined well. A multi-layered gas condensate reservoir model was constructed and simulated using actual reservoir rock and fluid properties. Effects of reservoir rock and fluid model simplification on inflow performance relationship (IPR) curves were investigated. Also, five different tubing pressure drop models were evaluated using extracted pseudo spontaneous potential (PSP) data from reservoir model to select the most accurate one for comput- ing tubing performance relationship (TPR) data. Then, accuracy of nodal analysis in prediction of well operating point was investigated through comparing with reservoir simulator results. Results of nodal analysis for this well indicated that a significant discrepancy exists between calculated and actual production rate. Sensitivity analysis on uncertainty parameters, skin factor and drainage radius, shows that skin factor of the investigated well varies between 11 and 12.9 for drainage radius in the range of 3000–20000 ft. Therefore, the problem of low well production rate was attributed to high skin factor as a result of formation damage. Also, results demonstrated that reduction of skin can lead to maximum 73% enhancement in daily volumetric gas production rate of well. Keywords Gas condensate well · Nodal analysis · Inflow performance relationship (IPR) · Tubing performance relationship (TPR) · Drainage radius · Skin factor Introduction of future generations are essential (Najibi et al. 2009). Non- normative withdrawals of reservoirs as well as drilling The worldwide demand for fossil fuels, especially natural numerous wells without any certain schedule cause exces- gas as an environmental friendly energy resource with eco- sive pressure drop of reservoirs and as a consequence low nomically feasible production, is annually increasing. Also, ultimate recovery (Shadizadeh and Zoveidavianpoor 2009). given the fact that economy of many countries depends on The best way to avoid such problems is an integrated res- oil and gas revenues, producing a certain daily volume of ervoir-well production optimization, which ensures oil com- hydrocarbon while preserving reservoirs to meet the needs panies that drilled wells and surface facilities are working at their peak performance at all times to maximize production (Shadizadeh and Zoveidavianpoor 2009). Several parameters * Reza Azin can be considered in production optimization of hydrocarbon firstname.lastname@example.org reservoirs, including drilling schedule, number of producer and injector wells, pattern of well placement, production rate Department of Petroleum Engineering, Faculty of Petroleum, and surface facilities (Guyaguler and Gumrah 1999). Usu- Gas and Petrochemical Engineering, Persian Gulf University, Bushehr, Iran ally, these parameters are optimized using simple reservoir models as well as mathematical or programming techniques Department of Mechanical Engineering, Faculty of Petroleum, Gas and Petrochemical Engineering, Persian involving economic strategies. Take the work done by Lee Gulf University, Bushehr, Iran and Aronofsky in 1958 as one of the early studies in this Department of Chemical Engineering, Faculty of Petroleum, field. They maximized crude oil production from homoge- Gas and Petrochemical Engineering, Persian Gulf University, neous and simple reservoir models using a developed linear Bushehr, Iran Vol.:(0123456789) 1 3 Journal of Petroleum Exploration and Production Technology programming for the optimization problem (Lee and Aro- (production rate and pressure) for the system with certain nofsky 1958). Bohannon in 1970 optimized efficiency of a characteristics which satisfies both inflow and outflow com - designed system having several oil reservoirs producing in ponents. Therefore, oil and gas wells should produce in their one or more gathering systems named as “multi-reservoir operating point conditions to achieve maximum possible pipeline system”. He presented a linear programming model efficiency. Application of nodal analysis has contributed to to define the optimum 15-years development plan for this ameliorate drilling and completion techniques, production designed system (Bohannon 1970). Also, the optimal type, and efficiency of many gas and oil systems. Works done by location and trajectory of an unconventional well for the Shadizadeh and Zoveidavianpoor in 2009 (Shadizadeh and different reservoir types and fluid systems were determined Zoveidavianpoor 2009), Dmour in 2013 (Dmour 2013) and by Yeten et al. in 2002. They applied an optimization pro- Soleimani in 2017 (Soleimani 2017) are brilliant examples cedure including genetic algorithm for their goal (Yeten for the usage of this approach. et al. 2002). Furthermore, Onwunalu and Durlofsky in 2011 There are many gas and oil wells around the world which developed a new well pattern optimization procedure for do not produce in their operating conditions for different rea- large-scale field development by utilizing particle swarm sons. Investigation performed on drilled wells in South Pars optimization technique (Onwunalu and Durlofsky 2011). In gas field located in Persian Gulf showed that most of them 2016, Nozohour-leilabady and Fazelabdolabadi maximized produce in low rate with unknown reason. On this subject in the Net Present Value for designed scenarios with multiple the current study, one of the wells in South Pars gas field is injector and producer wells and cases with deviated wells selected as a case study. According to available well data and in a real reservoir model. Artificial bee colony optimization challenges of production data analysis, an innovative and technique was used in their study (Nozohour-leilabady and integrated procedure based on nodal analysis is designed and Fazelabdolabadi 2016). Recently, a comprehensive produc- employed for production optimization and troubleshooting tion optimization study for an oil field located in the Middle the well problem. It is worth noting that complexities and East was done by Izadmehr et al. In their study, different fac- challenges of production data analysis in this reservoir are tors influencing oil production such as artificial lift model, addressed by Heidari Sureshjani et al. (Heidari Sureshjani water injection flow rate, drilling new producer and injector et al. 2016), Lak et al. (Lak et al. 2014), and Azin et al. wells and gas injection were examined in different scenarios (Azin et al. 2014) in six general steps, including data gath- through reservoir simulation to choose the optimized plan ering/extraction/quality check, choke modeling, well rate (Izadmehr et al. 2017). determination, well bottom-hole pressure estimation, layer Among the existing production optimization meth- rate allocation, and reservoir property estimation. In next ods, nodal analysis is the well-known and most powerful parts, methodology for generating IPR and TPR curves as approach in production engineering for optimization process two main tools of this research is described first, followed of oil and gas systems (Dale 1991). For the first time in by assessing the impacts of reservoir rock and fluid model 1954, Gilbert presented and used nodal analysis approach for simplification on IPR curves. Next, all necessary tools for the optimization of fluid production from reservoirs (Gilbert accomplishing nodal analysis are calculated. Then, the pro- 1954). Nodal analysis considers the reservoir-wellbore sys- posed methodology is validated for the well under study. tem, simultaneously. A reservoir with certain specifications Finally, sensitivity analysis is performed to figure out pos- (porosity, permeability, thickness, etc.) delivers the fluid into sible sources of low production rate. Concluding remarks the bottom hole of the well under defined operating condi- appear at the end. tions (flow rate and pressure). This fluid must overpass from the bottom to the top of the well and then surface facilities. This path from the bottom to the top of the well has many Methodology joints, valves, etc., that cause a pressure drop. Nodal analysis utilizes the computation of pressure drop across each section In this section, first the gas condensate reservoir simula- (from the reservoir to surface) to estimate production rate tion and procedure for generating IPR curves are explained. with regard to the existing conditions (Gilbert 1954). Pres- Then, details of TPR curve generation for nodal analysis sure drop of fluid flow across the porous media and tubing through well simulation are presented. are described by inflow (IPR) and outflow or tubing (TPR) performance relationship. Incorporating TPR curve with IPR Reservoir simulation provides an intersection which shows the well deliverabil- ity (also called well operating point or natural flow point) A sector of heterogeneous, two-dimensional, radial and for a system with defined reservoir and wellhead pressure multi-layered model of the investigated gas condensate (Dale 1991). This well operating point obtained through the field is constructed using real fluid and rock properties. For nodal analysis, represents optimum production condition this purpose, commercial reservoir simulator CMG, version 1 3 Journal of Petroleum Exploration and Production Technology 2012.10 is utilized. In this study, the module of IMEX and GEM are used for a modified black-oil and compositional simulation of the studied reservoir. Thermodynamic reser- voir fluid behavior is simulated using WINPROP module of CMG package. The reservoir contains lean gas with com- position shown in Table 1. Properties of plus fraction com- ponent including molecular weight and specific gravity are 214.89 g/mol and 0.835, respectively. Peng-Robinson equa- tion of state (PR-EOS) is applied for phase behavior studies of reservoir fluid. The phase envelope of main reservoir fluid is shown in Fig. 1. Details of EOS tuning using measured Pressure–Volume–Temperature (PVT) experimental data are described by Osfouri et al. (Osfouri and Azin 2016; Osfouri et al. 2015) (Table 2). Fig. 1 Phase diagram of reservoir fluid The studied reservoir is heterogeneous and multi-layered. Petrophysical specifications of each layers of studied res- ervoir including vertical (K ) and horizontal (K ) perme- an uncertainty exists in values of drainage radius and skin v h factor. It is prevalent to determine these uncertain param- abilities, porosity ( ) and thickness (h) are given in Table 2. In the base constructed model, a vertical well is located eters accurately through history matching of the simulation model to actual reservoir. Nevertheless, due to the lack of at the center of reservoir model and perforated along the whole reservoir thickness. Grid model was designed in radial coordinate. This designed grid model has 100 grid blocks in Table 2 Petrophysical specification of reservoir layers radial direction and their size increases logarithmically with distance from well. In other words, fine grid blocks were Layer K , mD K , mD h, ft h v used in near wellbore region to accurately model the effect 1 0.1166 0.0559 0.0169 117 of condensate banking and two-phase flow on well pro- 2 18.6542 0.0985 0.0764 51 ductivity. The coarse grids were employed at distances far 3 16.6094 0.0709 0.0633 67 from well where single-phase flow regime prevails. Water 4 0.1658 0.0444 0.0148 69 phase in reservoir is in an immobile state. Relative perme- 5 0.1065 0.0004 0.0010 51 ability curves of gas and condensate phases are illustrated 6 38.4135 0.1538 0.0671 36 in Fig. 2. Drainage radius and skin factor of the reservoir 7 35.3243 0.1208 0.0971 36 are 3280 ft and 0, respectively. It should be mentioned that 8 41.0909 0.1422 0.1011 45 9 0.0760 0.0003 0.0011 25 10 4.5335 0.0728 0.0575 9 Table 1 Composition of Component Mole (%) 11 33.7305 0.2363 0.1071 19 reservoir fluid H S 0.12 12 31.7728 0.3967 0.1107 28 13 3.2442 0.0676 0.0405 74 CO 1.92 N 3.51 14 0.1285 0.0508 0.0148 63 15 0.2069 0.0560 0.0222 132 C 82.79 C 5.35 16 0.1012 0.0475 0.0197 39 17 1.4744 0.1465 0.1102 16 C 2.00 iC 0.43 18 0.0667 0.0005 0.0339 16 19 3.8710 0.0931 0.0753 48 nC 0.72 iC 0.32 20 10.2853 0.2699 0.1236 47 21 19.1637 2.3491 0.2082 47 nC 0.29 C 0.39 22 17.1848 2.0416 0.2313 47 23 5.5656 0.1236 0.1058 23 C 0.48 24 16.1507 0.2029 0.0559 32 C 0.45 25 18.6719 2.0149 0.1401 63 C 0.29 26 30.5272 0.2372 0.1406 32 C 0.22 0.15 27 1.8467 0.0829 0.0685 133 28 0.1939 0.0520 0.0178 67 C 0.57 12+ 1 3 Journal of Petroleum Exploration and Production Technology 2014; Fevang and Whitson 1996; O’Dell 1967; Orodu et al. 2012). However, these models are insufficient to account for condensate accumulation and complex flow behavior in this region (Jokhio and Tiab 2002; Sakhaei et al. 2017). Actual conditions of near wellbore area in gas condensate reservoirs such as effect of high flow rate, high capillary number, non- Darcy ee ff cts and reservoir heterogeneity are not considered in these models (Kumar et al. 2006). These assumptions can cause significant error in predicting performance of wells. Therefore, gas condensate reservoir performance may be predicted with high accuracy and less assumptions through numerical simulation of a radial, single-well and hetero- geneous model with fine grid in near wellbore to consider all phenomena in this area. An example of IPR construc- tion through reservoir simulation is given by Sakhaei et al. Fig. 2 Gas/oil relative permeability curves (Sakhaei et al. 2017). A similar approach was used in this study to generate data points to plot IPR curves by simu- Table 3 Conditions of the base constructed reservoir model lation. This approach includes (1) constructing a reservoir model, followed by running the model at several different Initial reservoir pressure, Pisa 5280 bottom-hole pressures (well production with constant bot- Reservoir temperature, K 375 tom-hole pressure), (2) continuous recording of gas produc- Dew point pressure, Pisa 4500 tion rate as a function of average reservoir pressure in each Maximum liquid dropout, % 2.5 bottom-hole pressure and (3) running the model at each step Wellbore radius, ft 0.29 until average reservoir pressure reaches to the bottom-hole Total thickness, ft 1430 pressure. Therefore, a series of bottom-hole pressure data Reservoir depth, ft 3000 will be obtained as function of gas production flow rate at Connate water saturation 0.25 different average reservoir pressures. Grid number in r, θ and z direction 100,1,28 Well simulation proper and sufficient actual data, back-calculation method The pressure drop needed to lift reservoir u fl ids to the surface was employed to obtain data for nodal analysis. At the end, at a certain rate controlled by wellhead choke, is another sig- validity of the constructed reservoir model is checked. Other nificant factor affecting well deliverability. This pressure drop features of the constructed model are reported in Table 3. is determined based on the mechanical energy equation for One of the operational tools for evaluating performance flow between two points. In this regard, pressure drop along of wells in petroleum engineering is IPR curve. IPR for a the tubing is a function of mechanical configuration of the well is the relationship between flow rate of the well (Q ) and wellbore, properties of fluids and production rates (Orkisze- flowing pressure of the well or bottom-hole pressure (P ) wski 1967). The relationship between pressure drop along wf at certain average reservoir pressure (P ). Study of behavior the tubing and production rate is called TPR and is valid for and changes in IPR is essential in petroleum engineering. a defined wellhead pressure (Ikoku 1992). For plotting TPR Because, these curves are used for consideration of differ - curve, it is necessary to calculate bottom-hole pressure (P ) wf ent operating conditions, specification of optimum produc- at various production rates (Q) for a certain wellhead pressure tion rate and also design of production and artificial lift (P ). Given the fact that multiphase flows occur in almost wh equipment (Gilbert 1954; Golan and Whitson 1991). Some all gas and oil wells (Rai et al. 1989), several empirical/ana- numerical/analytical models with special assumption have lytical correlations have been developed to estimate pressure been developed based on Darcy’s equation for calculation drop in multiphase flow depending on reservoir and well con- of IPR curve mostly in oil or dry gas wells (Al-Attar and ditions, tubing and production rate (Ansari et al. 1990; Aziz AL-Zuhair 2008; Brar and Aziz 1978; Chase and Alkandari and Govier 1972; Baxendell and Thomas 1961; Beggs and 1993; Evinger and Muskat 1942; Fetkovich 1973; Mishra Brill 1973; Fancher Jr and; Brown 1963; Gray 1974; Hage- and Caudle 1984; Vogel 1968). Nevertheless, many inves- dorn and Brown 1965; Hasan and Kabir 1988; Mukherjee tigators generalized these numerical / analytical models for and Brill 1985; Poettman and Carpenter 1952). Selection of calculation of IPR curves in gas condensate wells consider- optimum correlation among these correlations are essential to ing two-phase flow in near wellbore region (Al-Shawaf et al. estimate pressure drop along tubing, plot TPR curve, evaluate 1 3 Journal of Petroleum Exploration and Production Technology well performance, determine operating point, design suitable reliability of this method were assessed. Eventually, the main surface facilities and production optimization. reason for the problem of low production rate was determined In this study, multiphase flow simulation of the well is uti- using this approach and through sensitivity analysis. lized to select proper correlation to calculate pressure gradi- ent along the objective gas condensate well. For this purpose, Simplification of the reservoir rock and fluid model Schlumberger PIPESIM software version 2008.1 is applied. Necessary input data into PIPESIM software includes required Reservoir simulation is an applicable tool for predicting the data for simulation of phase behavior of fluid, inflow perfor - reservoir performance under different scenarios in the least mance of the vertical well, tubing and fluid flow within the possible time and cost compared with studies on real fields. tubing. Compositional model is suggested for simulation of However, its application for some situations such as reservoirs thermodynamic behavior of gases by PIPESIM (Schlumberger with intricate phase behavior (gas condensate and volatile oil 2008). Therefore, phase behavior of fluid within the well was reservoirs) or heterogeneous and multi-layered formation is simulated using the composition of reservoir fluids presented very time-consuming and practically impossible. In this study, in Table 1 and PR-EOS. Also, reservoir temperature and static compositional simulation of 28-layer gas condensate reservoir pressure needed for simulation of inflow performance of the caused a significant jump in runtime due to the high volume of well were mentioned in previous section. Furthermore, the EOS and flash calculations in heterogeneous reservoir model IPR curve extracted from reservoir model was imported to with large number of grid blocks. In this regard, the reservoir PIPESIM as field data to find suitable and accurate model fluid and rock model were simplified and examined in different for estimating IPR data in constructed well model. Among states to choose a suitable one which gives satisfactory output. available models in PIPESIM, back-pressure model (Schlum- Typically, compositional simulators are used for simulating berger 2008) has best match with numerical/ empirical data. gas condensate and volatile oil reservoirs due to the impor- Data needed for simulation of tubing is given in Table 4. For tance of changes in composition of these reservoir fluids simulating fluid flow within the tubing and selecting optimum (Jamal et al. 2006). However, in many cases, simulation of pressure drop model, pseudo spontaneous potential (PSP) data compositional model for these types of reservoirs is not neces- elicited from reservoir model, as another empirical data, is sary. For an optimal performance, an intermediate simulator brought into software. By calculating PSP data in defined well- between standard black-oil and compositional, called modified head pressure and production rate and comparing with elicited black-oil, can be used. In this way, the volume of calculations data, optimum model for predicting pressure drop along tub- decreases remarkably (El-Banbi et al. 2006). Hence, after ing is selected. It is vital to note that empirical correlations of simulating thermodynamic behavior of reservoir fluid, com- Hagedorn and Brown (HBR) (Hagedorn and Brown 1965), positional as well as modified black-oil model were exported Mukherjee and Brill (MB) (Mukherjee and Brill 1985), Gray from WINPROP to import to GEM and IMEX and results (Gray 1974), Ansari et al. analytical model (Ansari et al. 1990) were compared. and NOSLIP correlation (Schlumberger 2008) were selected Furthermore, the actual 28-layer reservoir model was for comparison. Similar approach was applied in previous simplified to a single-layer model. The average porosity and work (Azin et al. 2016). permeability of the single-layer model were calculated by implementing average properties of 28-layer model (Table 2) Results and discussion using Eqs. (1)–(3). The average petrophysical specifications of single-layer model are reported in Table 5. The single-well model was constructed using real fluid and �h rock properties. Back-calculations were employed to plot IPR �= ∑ (1) curves and elicit other data necessary for selecting the opti- mum pressure drop model in tubing and performing nodal analysis. The conceptual structure of integration procedure K h used in this study for production optimization of the gas hi i K = ∑ (2) condensate well is shown in Fig. 3. According to this figure, after running necessary tools for nodal analysis, accuracy and K = v ∑ h (3) Table 4 Vertical well i Parameter Value specification vi True vertical depth, ft 4430.8 According to the explained procedure in Sect. 2.1, IPR Tubing roughness 0.0018 curves were plotted and compered in four different average Tubing diameter, in 6 1 3 Journal of Petroleum Exploration and Production Technology Fig. 3 Proposed strategy for integrated well performance analysis 1 3 Journal of Petroleum Exploration and Production Technology Table 5 Average petrophysical specification of single-layer reservoir Table 6 Relative errors P , psi Relative model between modified black-oil and errors, % compositional simulators in Main layer Sub-layer K , mD K , mD h, ft h v predicting production rate for 5000 2 single-layer reservoir model SL 1–28 9.68 0.00 0.066 1430 4000 5 3000 7 2000 7 Table 7 Average petrophysical specification of the 4-layer reservoir model Main layer Sub-layer K , mD K , mD h, ft h v ML1 1–5 5.90 0.0024 0.0315 355 ML2 6–9 31.56 0.0017 0.0735 141 ML3 10–18 4.75 0.0099 0.0393 396 ML4 19–28 10.06 0.1304 0.1075 538 model in other parts of this study. Also, results illustrated in Fig. 4 and Table 6 state that for average reservoir pres- sure above dew point pressure, the error between these two Fig. 4 Comparison of modified black-oil and compositional simula- tors for single-layer reservoir model simulators is insignificant. This is due to small changes in reservoir fluid composition at pressures higher than dew point pressure with low rate of retrograde condensation. reservoir pressures (P ) through compositional and modi- The relative error was calculated using Eq. (4): fied black-oil simulation of single-layer reservoir model. est act Q − Q These results are demonstrated in Fig. 4. It should be 100 i i RE%= (4) act mentioned that only reservoir rock and fluid model were i=1 i simplified and other specifications such as the number of est act grid blocks in the radial direction, well perforation, well- where, N is the number of points. Q And Q are esti- i i bore radius and reservoir pore volume were the same in all mated well production rate using modified black-oil and cases. Also, IPR curves were plotted by running reservoir compositional simulator in the same bottom-hole pressure, model at similar bottom-hole pressures for both simula- respectively. tors. As observed from Fig. 4, the IPR curve moves down- Another option for alleviating the number of reservoir ward by decreasing average reservoir pressure. In other layers is reconstruction of the 28-layer as 4-layer model. words, for a specific bottom-hole pressure, well produces Table 2 shows that layers 5, 9 and 18 have very low verti- a lower rate at lower average reservoir pressure. Also, in cal permeability. These low permeable layers act as a bar- defined average reservoir pressure, when the bottom-hole rier for exchanging flow between reservoir layers. There- pressure becomes close to average reservoir pressure, flow fore, it is expected that adjoining layers have different rate decreases and becomes zero due to absence of any pressure distribution along the reservoir drainage radius. pressure drawdown. Maximum flow rate, i.e., absolute However, embedded layers between two low permeable open flow (AOF) potential, happens when bottom-hole layers have almost the same pressure distribution due to pressure tends to be zero. According to Fig. 4, for the tar- their high vertical permeability. So, these layers can be get gas condensate reservoir, compositional and modified considered as one main layer. That is to say, the actual black-oil simulator have good agreement with each other 28-layer model was restored as 4-layer. Like single-layer in estimation of flow rate in various bottom-hole pressure. model, average specifications of 4-layer model were deter - The relative errors of estimated IPR curves using these two mined by utilizing Eqs. (1)–(3). Characteristics of 4-layer simulators are reported in Table 6. These reported errors model as well as sub-layer of each main layer are presented of less than 10% show that selecting modified black-oil in Table 7. It is vital to note that simplification of 28-layer simulator instead of compositional gives good results with reservoir model to 4-layer decreased runtime in compo- significantly lower runtime. So, the modified black-oil as sitional simulator slightly. Considering the fact that each an optimal simulator was utilized for running the reservoir 1 3 Journal of Petroleum Exploration and Production Technology Fig. 5 Comparison of a single-layer and b 4-layer reservoir model with the actual 28-layer model Table 8 Relative errors of single-layer and 4-layer reservoir model in predicting production rate P , psi Relative errors, % (single- Relative layer) errors, % (4-layer) 5000 14 1.0 4000 23 2.5 3000 33 3.0 2000 37 3.5 point of IPR curves is achieved in separate runs, likewise, extracting IPR curves from compositional simulation of 4-layer model were time-consuming and difficult. Modi- fied black-oil simulator with acceptable error required less Fig. 6 Average pressure distribution of reservoir layers with depth runtime for both 4- and 28-layer reservoir models. Figure 5 shows extracted IPR curves from modified black- est oil simulator for 1-, 4- and 28-layer reservoir models in the the difference that Q is estimated production rate of 1- or act same conditions. According to Fig. 5a, a substantial differ - 4-layer model. Q is well production rate in 28-layer model. ence exists between estimated flow rate of single-layer and Therefore, oversimplification of a multilayer reservoir into real 28-layer reservoir model in almost all bottom-hole pres- a single layer leads to a non-realistic IPR model which may sures. However, 4-layer model is in good agreement with result in an operating point different from that observed in results of 28-layer model, as shown in Fig. 5b. For a closer a gas well. examination, the relative errors of estimated production rate To better explain the reason for these observations, aver- of single-layer and 4-layer reservoir model with respect to age pressure distribution of reservoir layers with depth of 1-, results of 28-layer model are provided in Table 8. As seen, 4- and 28-layer model in average reservoir pressure of 4650 single-layer model has a relatively high error in well produc- psi and bottom-hole pressure of 900 psi were plotted and tion rate. Also, this error increases with decreasing average compared simultaneously. These results are demonstrated in reservoir pressure. The reported relative errors for 4-layer Fig. 6, which indicates that the average pressure in layers of reservoir model confirm the observed results of Fig. 5b. single-layer and 28-layer models are far from each other. The Equation (4) was used for calculation of relative error with lack of exchanging flow between reservoir layers because of 1 3 Journal of Petroleum Exploration and Production Technology existence of almost non-permeable layers (5, 9 and 18), leads (Gray 1974), Ansari et al. analytical model (Ansari et al. a discontinuity in pressure distribution of 28-layer model 1990) and NOSLIP correlation (Schlumberger 2008) were (Fig. 6). Therefore, the behavior of actual 28-layer model is selected to define the most accurate one. PIPESIM software not close to the single-layer one. In opposite, if the vertical recommends the HBR correlation (Hagedorn and Brown permeability is high in a multi-layered heterogeneous reser- 1965) for gas condensate wells due to the comprehensive- voir, exchange of flow occurs between layers and pressure of ness of data used to develop this model (Schlumberger layers approaches equilibrium. In such situation, the behav- 2008). Also, the Gray’s model is developed for gas con- ior of multi-layered reservoir will be close to a single-layer densate wells (Gray 1974). Furthermore, literature indicates and homogeneous reservoir. In this study, different pressure that correlations which use average values of liquid and gas distributions caused a significant discrepancy between pre- phase properties to calculate pressure drop have strong per- dicted well production rates and IPR curves of single-layer formance for a wide range of conditions (Kabir and Hasan and 28-layer model. As seen in Table 8, this difference is 2006). Gray’s empirical correlation (Gray 1974) and Ansari higher at lower reservoir pressure due to more extension of et al. analytical model (Ansari et al. 1990) are examples of condensate accumulation region and as a result, higher dif- these correlations. Also, MB (Mukherjee and Brill 1985) ferences in pressure distribution. Also, Fig. 6 shows that the and NOSLIP correlations (Schlumberger 2008) have been 4-layer model pressure distribution is close to the 28-layer suggested by Azin et al. (Azin et al. 2014, 2016) for comput- model. It is the main reason for high accuracy of this model ing pressure drop of gas condensate wells. in estimating well production rates. The PSP data consisting of pressure distribution with depth in the well were utilized to examine accuracy of the Nodal analysis mentioned correlations. PSP data actually are gained using downhole production logging tool. The production logging As mentioned, nodal analysis is a well-known approach in tool incorporates different electrical probes and measure- production engineering that can be used to improve perfor- ment tools for recording flow rate, fluid velocity, fluid mance of gas and oil systems. IPR curves, as one of the main type, density, temperature and pressure profile in different tools in this approach, were calculated through simulation flow rates (Eisa et al. 2013). In designed strategy for well of the reservoir fluid flow and presented in the previous sec- performance analysis (Fig. 3), this pressure profile was tion. Also, the gas condensate well simulation was applied obtained through running the reservoir model (the modi- to determine the optimum pressure drop model in tubing and fied black-oil simulation of 28-layer model) with the well calculate TPR curves. Five pressure drop models including producing at a constant flow rate (60 and 120 MMSCFD). Hagedorn and Brown (HBR) (Hagedorn and Brown 1965), These measured data through reservoir simulation as Mukherjee and Brill (MB) (Mukherjee and Brill 1985), Gray well as estimated gradient pressure using five mentioned Fig. 7 Comparison of tubing pressure drop models in a Q = 60 MMSCFD and b Q = 120 MMSCFD 1 3 Journal of Petroleum Exploration and Production Technology Table 9 Accuracy of tubing pressure drop models in comparison with a relative error of less than 3%, and the MB correlation measured data (Mukherjee and Brill 1985) has the lowest accuracy. Among three correlations with highest accuracy, Gary’s Pressure drop model Relative error, % model (Gray 1974) was selected as the optimum pressure Q = 60 MMSCFD Q = 120 drop model to calculate TPR curves for the studied well. MMSCFD TPR curves were plotted at four specified wellhead pres- Ansari et al. (Ansari et al. 1990) 0.67 2.08 sures of 600, 1500, 2500 and 3500 psi. Nodal analysis Gray (Gray 1974) 1.88 2.31 was performed using these TPR curves and calculated IPR HBR (Hagedorn & Brown 1965) 5.40 6.95 curves for the 28-layer reservoir model to ascertain the NOSLIP 2.59 2.01 operating points of well at different average reservoir pres- MB (Mukherjee & Brill 1985) 13.90 13.03 sures and flowing wellhead pressures. Results are shown in Fig. 8 for different reservoir pressures. At a given aver - age reservoir pressure (P ) and flowing wellhead pressure (P ), intersection of TPR and IPR curves represent well wh operating point. According to Fig. 8, the operating point of well changes by shifting both the IPR and TPR curves when the fixed pressures (P or P ) in the system with r wh specified properties (tubing size, etc.) are changed. Reser - voir depletion and as a result decline in reservoir pressure causes the intersection of IPR and TPR curves move down- ward at a certain wellhead pressure. Take the results for plotted TPR curve at P = 600 psi in Fig. 8 as an exam- wh ple. In some situations, there is no intersection between the IPR and TPR curves in the operating condition, like when the reservoir pressure declines to 2000 psi and wellhead pressure is 2500 psi. This represents that the well will not flow under these reservoir conditions. Therefore, different solutions for this problem should be investigated to elevate Fig. 8 Nodal analysis for the 28-layer reservoir model well productivity in present or future life of the well. Solu- tions include decreasing the wellhead pressure, changing pressure drop models are demonstrated in Fig. 7 for two the tubing size or installing artificial lift equipment. The different production rates. Pressure drop calculations were values of production rate and bottom-hole pressure cor- begun from the highest possible point at depth of 3000 ft. responding to natural flow points of the well at different As seen in Fig. 7, the Ansari et al. (Ansari et al. 1990), conditions are reported in Table 10. Gray (Gray 1974) and NOSLIP (Schlumberger 2008) cor- To assess the validity of obtained operating points using relations show good match for estimation of measured nodal analysis (Table 10), these points were directly com- data in both production rates, while HBR (Hagedorn and puted through reservoir simulation. For this purpose, the Brown 1965) and MB (Mukherjee and Brill 1985) cor- 28-layer reservoir model was run at four different constant relations deviate from measured data. The relative errors wellhead pressures (600, 1500, 2500 and 3500 psi). When of each model in different production rates are presented the average reservoir pressure reached 2000, 3000, 4000 in Table 9. This table shows that Ansari et al. (Ansari and 5000 psi, the operating points were extracted from et al. 1990), Gray (Gray 1974) and NOSLIP (Schlum- reservoir simulator. These elicited operating points are berger 2008) correlations anticipate the pressure drop with presented in Table 11 for different operating conditions. Table 10 Operating points through nodal analysis for 28-layer reservoir model P , psi P = 5000 psi P = 4000 psi P = 3000 psi P = 2000 psi wh r r r r Q, MMSCFD P , psi Q, MMSCFD P , psi Q, MMSCFD P , psi Q, MMSCFD P , psi wf wf wf wf 600 410.4086 3001 295.1422 2226 206.5070 1639 120.2845 1099 1500 383.2343 3178 259.7290 2471 160.5800 1994 – – 2500 323.3958 3572 177.8528 2989 – – – – 3500 229.9897 4129 – – – – – – 1 3 Journal of Petroleum Exploration and Production Technology Table 11 Operating points through reservoir simulation P , psi P = 5000 psi P = 4000 psi P = 3000 psi P = 2000 psi wh r r r r Q, MMSCFD P , psi Q, MMSCFD P , psi Q, MMSCFD P , psi Q, MMSCFD P , psi wf wf wf wf 600 410.5144 3040 303.6800 2550 217.7679 1666 124.0269 1141 1500 385.2462 3205 269.3775 2484 170.3649 1998 – – 2500 325.7036 3583 185.9858 2990 – – – – 3500 231.4046 4128 – – – – – – Table 12 Percentage of relative P , psi P = 5000 psi P = 4000 psi P = 3000 psi P = 2000 psi wh r r r r error of nodal analysis in predicting production rate and Q P Q P Q P Q P wf wf wf wf bottom-hole pressure for the 600 0.02 1.28 2.81 1.02 5.17 1.57 3.02 3.75 28-layer reservoir model 1500 0.52 0.84 3.58 0.55 5.74 0.18 – – 2500 0.70 0.32 4.37 0.05 – – – – 3500 0.70 0.02 – – – – – – Table 12 shows the relative errors of nodal analysis com- pared to reservoir simulation in determining production rates and bottom-hole pressures of operating points at various operating conditions. According to this table, nodal analysis has a negligible error in forecasting operating points com- pared to numerical reservoir simulation. Overall, accuracy of nodal analysis in prediction of the operating point reduces by decreasing average reservoir pressure. This increased error can be attributed to the extension of condensate bank, two- phase flow in the near wellbore area and differences in pro- duction history of reservoir model. Figure 9 shows application of nodal analysis for single- layer and 4-layer reservoir models. The operating points for simplified reservoir models are reported in Table 13. As Fig. 9 Nodal analysis for the single-layer and 4-layer reservoir mod- expected, the operating points by nodal analysis in 4-layer els model shows better results than single-layer model compared Table 13 Operating points through nodal analysis for single-layer and 4-layer reservoir model P , psi P = 5000 psi P = 4000 psi P = 3000 psi P = 2000 psi wh r r r r Q, MMSCFD P , psi Q, MMSCFD P , psi Q, MMSCFD P , psi Q, MMSCFD P , psi wf wf wf wf Single-layer 600 433.3725 3158 325.9187 2431 239.8809 1859 144.3980 1243 1500 408.7104 3333 292.1207 2646 193.7127 2140 – – 2500 351.1414 3706 210.1653 3098 – – – – 3500 258.3900 4219 – – – – – – 4-layer 600 410.9239 3004 293.2625 2214 202.0954 1611 117.5400 1082 1500 387.2530 3203 256.9339 2456 156.3771 1976 – – 2500 325.2180 3580 175.2143 2981 – – – – 3500 229.6670 4118 – – – – – – 1 3 Journal of Petroleum Exploration and Production Technology to reservoir simulator (Table 11). The average relative errors of nodal analysis for single-layer and 4-layer reservoir mod- els compared to reservoir simulation are 10 and 3.61%, respectively. Problem of low gas production rate in an inclined well In this part, nodal analysis is performed on an inclined gas well drilled in the supergiant offshore gas condensate field, which penetrates along 1112 ft of total reservoir production region (1430 ft), completed as open-hole. Vertical well pen- etration was changed to 1112 ft of total reservoir thickness in constructed reservoir model. Production rates from reservoir model were corrected for the inclined well conditions using the Fig. 10 Comparison of actual and calculated operating points Peaceman’s model (Peaceman 1983). Details of this method are provided in the appendix. Also, the constructed well model simulated cases in Table 15. Also, TPR curve appertains was modified using actual values of true vertical depth (1112 ft) and measured depth (1778 ft) of the inclined well. to wellhead pressure and physical conditions of the tubing and was unchanged in all cases. Gray’s model (Gray 1974) Actual operating conditions of target well are reported in Table 14. Figure 10 shows results of nodal analysis for the was suggested to model inclined wells (Azin et al. 2016), and was used in this section. Figure 11 shows results of objective well and comparison of real and calculated operat- ing points. According to this figure, actual production rate nodal analysis for simulated cases according to Table 15. Well operating points in different simulated cases which has a remarkable difference with calculated production rate by nodal analysis. Rock properties, fluid properties, reservoir were achieved from intersection of IPR and TPR curves, are reported in Table 16. specifications, well geometry and well flowing pressure are principal factors affecting the IPR curve. TPR curve depends Results of Table 16 show that gas production rate is highly dependent on skin factor. However, variations in on wellhead pressure and physical conditions of the tubing (Beggs 1980). In this research, all these effectual factors were considered using real conditions of target well. How- Table 15 Categories for sensitivity analysis ever, uncertainty exists in the values of drainage radius and skin factor of investigated reservoir. In the prior sections, the Simulated case Skin factor Drainage radius, ft constructed reservoir model was run for drainage radius and Group # 1 skin factor of 3280 ft and 0, which are suspected to cause 1 0 5000 significant difference in well performance in real reservoir. 2 10 5000 Effects of these parameters on IPR curve and operating 3 20 5000 point were studied through sensitivity analysis. Variations 4 40 5000 of drainage radius and skin factor were divided into four Group # 2 groups (1, 2, 3 and 4) presented in Table 15. Skin factor is 5 0 10,000 set to change in the range of 0–40. The drainage radius were 6 10 10,000 5000, 10,000, 15,000 and 20,000 ft for group 1, 2, 3 and 4, 7 20 10,000 respectively. Totally, 16 different cases were run to perform 8 40 10,000 the sensitivity analysis. Group # 3 Since the IPR curve depends on reservoir and well con- 9 0 15,000 ditions, distinct IPR curves were obtained for each of the 10 10 15,000 11 20 15,000 12 40 15,000 Table 14 Actual operating Parameter Value conditions of the target well Group # 4 Q, MMSCFD 118 13 0 20,000 P , psi 4353 14 10 20,000 wf P , psi 3244 15 20 20,000 wh P , psi 5280 16 40 20,000 1 3 Journal of Petroleum Exploration and Production Technology Fig. 11 Nodal analysis for simulated cases in a group # 1, b group # 2, c group # 3 and d group # 4 drainage radius have insignificant impact on gas produc- where r , r and S are drainage radius, wellbore radius and e w tion rate. For more detailed investigation, the proposed skin factor. A is a function of rock permeability, reservoir relationship between gas flow rate and pressure by Rawlins thickness, average u fl id properties and reservoir temperature. and Schellhardt (Eqs. (5) and (6)) (Rawlins and Schellhardt For simplicity, exponent n in Eq. (5) was considered one. 1935) was utilized. According to Eq. (6), the coefficient C has an inverse rela- tionship with skin factor and logarithm of drainage radius. 2 2 The influence of drainage radius on production rate is neg- Q = C P − P (5) r wf ligible due to this logarithmic relationship, which confirms results of Table 16. Equation (5) can be rewritten as fol- C = lows to define the relationship between skin factor, drainage r (6) ln + S radius and gas production rate: 1 3 Journal of Petroleum Exploration and Production Technology Table 16 Well operating points for different simulated cases skin factor, logarithm of drainage radius and operating point can be expressed by Eq. (8) for the objective well. Simulated case Q, MMSCFD P , psi wf 2 2 Group # 1 P − P r wf ln r + S = 308.9946 − 2.5503 (8) 1 177 4604 2 122 4419 3 88.3 4340 Using actual operating conditions reported for target well 4 55.7 4288 in Table 14, Eq. (8) simplifies to Eq. (9 ): Group # 2 ln r + S = 20.88 5 172 4588 (9) 6 121 4416 Considering different values for skin factor, correspond- 7 88.2 4339 ing drainage radius was calculated by Eq. (9) to determine 8 56.1 4289 operating point, and results are shown in Table 17 as group Group # 3 (A) According to these results, for skin factor less than 10, 9 171 4582 the corresponding drainage radius is very large and unrea- 10 120 4415 sonable. On the other hand, for skin factor above 15, cor- 11 88.4 4340 responding drainage radius will be very short. By assuming 12 56.5 4289 logical values for drainage radius, corresponding skin factor Group # 4 was computed using Eq. (9) and summarized in Table 17 as 13 170 4579 group (B) Results of this table show that for drainage radius 14 120 4415 range of 3000–20,000 ft, the skin factor is variable between 15 88.4 4340 11 and 12.9, quite high for the investigated gas condensate 16 56.7 4289 well. So, the problem of low well production rate can be attributed to this high skin factor. Based on Table 17 (group B), skin factor is 11.67 for drainage radius of 10,000 ft. In this case, if skin factor 2 2 P − P r wf reduces to the values of 5 or 0, the gas production rate ln r + S = A + B (7) Q increases from 118 MMSCFD to 160 and 204 MMSCFD by considering the current value of bottom-hole pressure 2 2 P −P r wf and average reservoir pressure in Eq. (8). In other words, the According to Eq. (7), a plot of (ln r + S) vs. daily volume of gas production of this well would increase to yields a straight line with slope of A and y-intercept of B. 42–86 MMSCFD (maximum 73%). Hence, finding the rea- Figure 12 shows this straight line for the reported data in son for this high skin factor is essential as the first step before Table 16. According to this figure, the relationship between suggesting a suitable remedy for this problem. Accordingly, five different skin factors will be introduced and their exist- ence evaluated for the objective well. In the ideal conditions, a vertical well which is completed as open-hole, produces Table 17 Estimated skin factor Skin factor Drainage radius, ft and drainage radius for target well Group A 0 1.18E09 5 7.93E06 10 53,446 12 7233 15 360 Group B 12.88 3000 12.36 5000 11.67 10,000 11.27 15,000 2 2 10.98 20,000 P −P r wf Fig. 12 (ln r + S) vs. for the target well 1 3 Journal of Petroleum Exploration and Production Technology single-phase fluid from formation with no damage at a rate of this phase were included in the model. Hence, this type of determined by Darcy’s law (Ahmed and McKinney 2011). skin cannot be the reason for significant difference between There are five types of skin factor observed in real cases, calculated and actual gas production rate. including mechanical skin, completion pseudoskin, geomet- The last one is rate-dependent skin which occurs fre- rical pseudoskin, multiphase pseudoskin, and rate-dependent quently in high-rate gas wells and indicates deviation from skin frequently occur in hydrocarbon reservoirs (Ahmed and the Darcy’s law. The non-Darcy flow that occurs due to high McKinney 2011; Ezenweichu and Laditan 2015; Jianchun velocity and turbulence of flow in about 5–10 ft around the et al. 2014). wellbore causes the relationship between the flow rate and Mechanical skin factor refers to permeability reduction pressure to become non-linear (Huang and Ayoub 2008). due to formation damage through plugging the flow paths Effect of non-Darcy flow is applied in numerical simulation in porous formation with solid particles of drilling fluid or of reservoirs by considering rate-dependent skin. Including different process like well stimulation by acidizing (Ezen- this type of skin factor in the constructed reservoir model weichu and Laditan 2015; Jianchun et al. 2014). For the showed little or no impact on gas production rate, as shown objective well, no evidence is reported for formation dam- in Fig. 13. age. Completion pseudoskin addresses formation damage Among different sources of skin factor, the completion due to completion. Usually, the well completion as open- pseudoskin and rate-dependent skin are negligible accord- hole is the cheapest method and implies radial flow regime ing to the investigated reservoir and well conditions. Also, in the near wellbore area. Other completion techniques are geometrical and multiphase pseudoskin were included in the employed to isolate produced fluid from different layers or constructed reservoir and well models. Therefore, mechani- prevent water and gas coning (Holditch 1992). Furthermore, cal skin or formation damage could be the only reason for a well may partially penetrate to the formation. Partial well the high skin factor in studied gas condensate well. Mini- penetration and well completion using other methods than mizing this skin factor is the key to achieve high yield of open-hole cause flow regime become non-radial like spheri- gas production, which needs more study for finding a suit- cal or hemispherical flows (Ahmed and McKinney 2011). able remedy. Generally, as stated by Civan (Civan 2015), the Extra pressure drop due to well completion and penetration development of technologies and strategies for cost-effective is defined by the completion pseudoskin factor concept. As formation damage control and remediation is both a science mentioned, the target well of this study was completed as and an art. Literature show that there are no universally open-hole and completion pseudoskin does not exist for this proven technologies used as a remedy for all reservoirs. well. Nevertheless, creative approaches, supported by science and Geometrical pseudoskin arises when the well perfor- laboratory and field tests yield the best solution. Mechanical mance is influenced by well geometry. Geometry of wells high-pressure hydraulic fracturing (Keelan and Koepf 1977; are divided into vertical, horizontal, inclined, etc (Ismail Wang et al. 2017), chemical low-pressure treatment (Bridges and El-Khatib 1996; Kumar and Bryant 2008). The verti- 2000), formation acidizing (Martin 2004) and acoustic well cal well which penetrates totally in production formation stimulation (Kolle and Theimer 2010) are examples of the is known as base well. Any difference between base well more common treatment methods. productivity and wells with other geometry are referred as geometrical pseudoskin. In the constructed reservoir model, the well was considered as vertical well and production rates were corrected using Peaceman’s model (Peaceman 1983) for the inclined conditions. So, this type of skin factor cannot exist for the investigated well. Also, multiphase pseudoskin refers to skin caused by multiphase flow in the formation, especially near wellbore area, due to water and gas coning, gas production from liquid hydrocarbon or liquid production from gas condensate fluid. Multiphase flow is associated with higher drawdown pressure compared to single-phase. This extra drawdown pressure is known as multiphase pseu- doskin factor. In the gas condensate reservoir under study, the bottom-hole pressure is below the dew point. Therefore, multiphase flow occurs near wellbore and cause reduction of well deliverability. In the constructed reservoir model, fine grid blocks were used in the near wellbore region and vari- Fig. 13 Average reservoir pressure and gas production rate with and ations in gas saturation and decreasing relative permeability without rate-dependent skin 1 3 Journal of Petroleum Exploration and Production Technology Conclusion The objective of this study was to investigate the reasons for low production rate in a producing well of a supergiant gas condensate reservoir. An integrated strategy was pro- posed and employed for production optimization and trou- bleshooting the well problem. In this strategy, nodal analysis approach was used for investigation of well performance. IPR and TPR curves were plotted through reservoir and well simulation. Effects of simplifying reservoir rock and fluid model on IPR curves were assessed due to difficulties and the high amount of time consumed when extracting IPR curves from compositional simulation of 28-layer model. It was found that oversimplification of a multilayer reser - voir into a single layer leads to a non-realistic IPR model which may result in an operating point different from that observed in a gas well. Also, different pressure distributions caused a significant difference between the estimated well production rates from single-layer and 28-layer model. This difference increased by decreasing reservoir pressure. The Fig. 14 The inclined well path and its x-, y- and z-components 4-layer model had high accuracy compared to real reser- voir model and showed pressure distribution approximately similar to the 28-layer model. Five different tubing pressure Appendix drop models were examined using the rational elicited PSP data from reservoir model for selecting the optimal model. Usually, in the numerical simulation of hydrocarbon res- Among these correlations, the Gary’s model was found ervoirs, the Peaceman’s model is applied to calculate well as the optimum pressure drop model for computing TPR production rate (CMG 2012). According to this model, curves. Nodal analysis accuracy in prediction of well operat- well production rate is calculated using Eq. (10) (Peaceman ing point was confirmed through its good agreement with the 1983): results gained from running base constructed reservoir and Q = WI(P − P ) wb wf (10) well models. Results of nodal analysis for real inclined well where WI and P are well index and well block pressure, wb indicated that a striking difference exists between calculated respectively. This model is developed for vertical wells and and actual production rate. Sensitivity analysis conducted on needs be corrected for inclined wells. As seen in Fig. 14, the two uncertain parameters including skin factor and drainage inclined well path can be portrayed on X, Y and Z directions radius indicated that skin factor of investigated well is 11.67 of Cartesian coordinates. The well index can be computed for drainage radius of 10,000 ft. Therefore, the problem of in these three directions by utilizing length of the well image low well production rate was attributed to this high skin in each direction (L , L and L ) and the proposed model by x y z factor as a result of formation damage skin near wellbore. Peaceman for calculation of the equivalent radius (r ), as Also, results indicated that maximum 73% increment in gas o follows (Peaceman 1983): production of the well can be achieved by reduction of this skin factor. 2 K K (L ) y z x WI = � � (11) o,x Open Access This article is distributed under the terms of the Crea- ln + S tive Commons Attribution 4.0 International License (http://creat iveco mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- tion, and reproduction in any medium, provided you give appropriate 2 K K (L ) x z y credit to the original author(s) and the source, provide a link to the WI = � � (12) Creative Commons license, and indicate if changes were made. r o,y ln + S 2 K K (L ) x y z WI = � � (13) o,z ln + S 1 3 Journal of Petroleum Exploration and Production Technology Baxendell P, Thomas R (1961) The calculation of pressure gradients in 0.5 high-rate flowing wells J Petrol Technol 13:1023–021,028 0.5 0.5 2 z 2 Beggs HD (1980) Production Optimization. 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